Stable Liquid Hydrogen at High Pressure by a Novel Ab Initio Molecular-Dynamics Calculation

We introduce an efficient scheme for the molecular dynamics of electronic systems by means of quantum Monte Carlo. The evaluation of the (Born-Oppenheimer) forces acting on the ionic positions is achieved by two main ingredients: (i) the forces are computed with finite and small variance, which allows the simulation of a large number of atoms, (ii) the statistical noise corresponding to the forces is used to drive the dynamics at finite temperature by means of an appropriate Langevin dynamics. A first application to the high-density phase of hydrogen is given, supporting the stability of the liquid phase at $\simeq 300\mathrm{GPa}$ and $\simeq 400\mathrm{K}$.

Figure 1

Evolution of the integrand in Eq. (6) as a function of the Monte Carlo iterations. Each new sample is obtained after $2N$ Metropolis trials.

Figure 2

Evolution of the internal energy and temperature vs the AMD with QMC forces. $\Delta t={\Delta }_0=1.036\mathrm{fs}$, ${\alpha }_0=0.7k_{B}T\mathrm{a}.\mathrm{u}.$ Bottom: points represent instantaneous temperatures estimated by the average kinetic energy, lines represent the target temperatures. They should coincide on average for $\Delta t\to 0$. The average energy, pressure, and temperature in the last 0.5 ps are $-0.51319\pm 0.00003\mathrm{H}$ ($-0.5127\pm 0.0001\mathrm{H}$) $364\mathrm{K}\pm 5\mathrm{K}$ ($364\pm 10\mathrm{K}$) and $335\pm 2\mathrm{GPa}$ ($394\pm 5\mathrm{GPa}$) for $N=128$ ($N=16$), respectively. At each iteration the statistical noise on the total energy is $\simeq 5000\mathrm{K}$. The proton-proton $g(r)$, averaged at the lowest temperature, is shown in the inset.